Circadian clocks regulate biological behaviours, such as sleeping and waking times, that recur naturally on an approximately 24-hour cycle. These clocks tend to be influenced by a variety of external factors, sometimes to the extent that it can have an impact on health. As an example in pharmacology, the effects of chemicals on the circadian rhythm in patients can be key to clarifying the relationship of drug efficacy and toxicity with dosing times. While pre-clinical experiments conducted to elucidate these effects may produce correlated data measured over time, such as gene expression profiles, existing methods for fitting parametric nonlinear regression models are, however, inadequate and can lead to unreliable, inconsistent parameter estimates and invalid inference. De-trending is widely used as a pre-processing step to address non-stationarity in the data, before fitting models based on the assumption of independence. However, as it is unclear that this approach properly accounts for the correlation structure, alternative methods that specifically model the correlation in the data based on conditional least squares and a two-stage estimation procedure are proposed and evaluated. A simulation study covering a wide range of scenarios and models shows that the proposed methods are more efficient and robust against model mis-specification than de-trending and, furthermore, they reduced estimation bias in the circadian period and provide more reliable confidence intervals.
